Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization

被引：5

作者：

Berselli, Luigi C. ^{[1
]}

Fagioli, Simone ^{[2
]}

Spirito, Stefano ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Via F Buonarroti 1-C, I-56127 Pisa, Italy

[2] Univ Aquila, DISIM, Via Vetoio, I-67100 Laquila, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 125卷

关键词：

Navier-Stokes equations; Local energy inequality; Numerical schemes; theta-method; Finite element and finite difference methods; SLIP BOUNDARY-CONDITIONS; SEMI-DISCRETIZATION; PARTIAL REGULARITY;

D O I：

10.1016/j.matpur.2018.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the theta-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：189 / 208

页数：20

共 50 条

[21] Partial Regularity of Suitable Weak Solutions to the Fractional Navier-Stokes Equations
Tang, Lan
Yu, Yong
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 334 (03) : 1455 - 1482
[22] Suitable Weak Solutions to the Navier-Stokes Equations of Compressible Viscous Fluids
Feireisl, Eduard
Novotny, Antonin
Sun, Yongzhong
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2011, 60 (02) : 611 - 631
[23] Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations
Stephen Gustafson
Kyungkeun Kang
Tai-Peng Tsai
[J]. Communications in Mathematical Physics, 2007, 273 : 161 - 176
[24] QUANTITATIVE ESTIMATES FOR SPACE-TIME ANALYTICITY OF SOLUTIONS TO THE FRACTIONAL NAVIER-STOKES EQUATIONS
Wang, Cong
Gao, Yu
Xue, Xiaoping
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2023, 22 (08) : 2619 - 2645
[25] Analysis of a Full Space-Time Discretization of the Navier-Stokes Equations by a Local Projection Stabilization Method
Ahmed, Naveed
Chacon Rebollo, Tomas
John, Volker
Rubino, Samuele
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2017, 37 (03) : 1437 - 1467
[26] Space-time Euler discretization schemes for the stochastic 2D Navier-Stokes equations
Bessaih, Hakima
Millet, Annie
[J]. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2022, 10 (04): : 1515 - 1558
[27] A remark on weak-strong uniqueness for suitable weak solutions of the Navier-Stokes equations
Lemarie-Rieusset, Pierre Gilles
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2022, 38 (07) : 2217 - 2248
[28] On time analyticity of weak solutions of the compressible Navier-Stokes equations
Tsyganov, Eugene
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2007, 229 (02) : 97 - 103
[29] ON REGULARITY WITH RESPECT TO TIME OF WEAK SOLUTIONS OF NAVIER-STOKES EQUATIONS
GOLOVKIN, KK
KRZYWICK.A
[J]. COLLOQUIUM MATHEMATICUM, 1967, 16 : 163 - &
[30] On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations
Robinson, James
Sadowski, Witold
Sharples, Nicholas
[J]. IUTAM SYMPOSIUM ON TOPOLOGICAL FLUID DYNAMICS: THEORY AND APPLICATIONS, 2013, 7 : 161 - 166

← 1 2 3 4 5 →